Real-time battery estimation

ABSTRACT

Vehicle systems and methods can include a traction battery and a controller to implement a state estimator configured to output battery state based on internal resistance of the traction battery and a system dynamics estimation of the traction battery using discrete battery measurements of voltage and internal resistance, and operate the traction battery according to output of the state estimator. For example, the controller can identify a system dynamics model of the traction battery using a battery input current profile and a battery output voltage profile measured within a predefined time period, transform the identified system dynamics model to a state-space model having a diagonal system matrix consisting of system Eigenvalues through the Eigendecomposition, estimate battery current limits and available power limits from the transformed system dynamics model, and operate the traction battery according to system dynamics model identified using estimated battery current limits and available power limits.

TECHNICAL FIELD

Various embodiments relate to an electric vehicle and a method forestimating the state of a battery, specifically, estimating inreal-time, and using the battery estimation to control the vehiclesystems in view of the battery state.

BACKGROUND

Hybrid electric vehicles (HEV) utilize a combination of an internalcombustion engine with an electric motor to provide motive power. Thisarrangement provides improved fuel economy over a vehicle that has onlyan internal combustion engine. One method of improving the fuel economyin a HEV is to shutdown the engine during times that the engine operatesinefficiently, and is not otherwise needed to propel the vehicle. Inthese situations, the electric motor is used to provide all of the powerneeded to propel the vehicle. When the driver power demand increasessuch that the electric motor can no longer provide enough power to meetthe demand, or in other cases such as when the battery state of charge(SOC) drops below a certain level, the engine provides the motive powerfor the vehicle.

The HEV includes a battery management system that estimates valuesdescriptive of the battery pack and/or battery cell present operatingconditions. The battery pack and/or cell operating conditions includebattery SOC, power fade, capacity fade, and instantaneous availablepower. The battery management system should be capable of estimatingvalues during changing cell characteristics as cells age over thelifetime of the pack. The precise estimation of some values may improveperformance and robustness, and may ultimately lengthen the usefullifetime of the battery pack.

SUMMARY

A vehicle can include a traction battery including a plurality of cellsand at least one controller programmed to implement a state estimator.The state estimator can be configured to output battery state based oninternal resistance of the traction battery and a system dynamicsestimation of the traction battery using discrete battery measurementsof voltage and internal resistance, and operate the traction batteryaccording to output of the state estimator. In an example, the systemdynamics estimation applies a subspace identification algorithm toapproximate system matrices.

In an example, the controller uses the system matrices to derive acurrent limit expression. The controller can output battery currentlimits using estimated state variables and estimated internalresistance. In an example, the computed internal resistance is estimatedusing battery current input during a time period and the state variablesbeing estimated from the terminal voltage during the time period.

In an example, the controller can estimate the internal resistanceduring a time period, identify a discrete state space model by asubspace identification algorithm using a battery current input profileand a battery terminal voltage profile collected within a predefinedtime period, convert the discrete model to continuous state space model,perform Eigendecomposition of the system matrix of the continuous model,transform the state space model by the Eigendecomposition, and deriveanalytic expressions for computing battery current limits within apredefined time period.

The controller can also determine whether additional battery modelparameters need to be updated and if so repeat the process for theadditional battery model parameters.

In an example, a vehicle can include a at least one controllerprogrammed to identify a system dynamics model of the traction batteryusing a battery input current profile and a battery output voltageprofile measured within a predefined time period, transform theidentified system dynamics model to a state-space model having adiagonal system matrix consisting of system Eigenvalues through theEigendecomposition, estimate battery current limits and available powerlimits from the transformed system dynamics model, and operate atraction battery according to system dynamics model identified usingestimated battery current limits and available power limits.

In an example, the system dynamics model can include a system dynamicsmatrix, an input matrix and an output matrix. The system dynamics modelcan be identified using a subspace identification algorithm. In anexample, the subspace identification algorithm uses a voltage profilemanipulated by subtracting a voltage drop across a battery internalresistance from the battery output voltage profile. The computedinternal resistance can be estimated using battery current input profileduring the predetermined time period and the measured terminal voltageprofile during the time period.

In the vehicle or controller, the system dynamics model is updated inreal time.

Various methods can be performed with the vehicle and controller. In anexample, a method for vehicle control includes identifying a systemdynamics model of a traction battery using a battery input currentprofile and a battery output voltage profile measured within apredefined time period, transforming the identified system dynamicsmodel to a state-space model having a diagonal system matrix consistingof system Eigenvalues through the Eigendecomposition, estimating batterycurrent limits and available power limits from the transformed systemdynamics model, and operating the traction battery according to systemdynamics model identified using estimated battery current limits andavailable power limits.

In an example, the step of identifying the system dynamics modelcomprises identifying a system dynamics matrix, an input matrix and anoutput matrix.

In an example, the step of identifying the system dynamics modelincludes using a subspace identification algorithm

In an example, the step of identifying the system dynamics modelincludes using a voltage profile manipulated by subtracting a voltagedrop across a battery internal resistance from the battery outputvoltage profile.

In an example, the step of identifying the system dynamics modelincludes estimating the computed internal resistance using the batterycurrent input profile during the predetermined time period and themeasured terminal voltage profile during the time period.

In an example, the step of identifying the system dynamics modelincludes identifying the system dynamics model in real time.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a hybrid electric vehicle that can be used with the describedsystems and methods.

FIG. 2 is a detailed view of the battery for a hybrid electric vehicle.

FIG. 3 is a schematic of a system controller.

FIG. 4 is a flow chart of a method according to various examples.

FIG. 5 is a flow chart of a method according to various examples.

FIGS. 6A-6D are various graphs of vehicle parameters, actual andestimated according to an example.

FIGS. 7A-7B are various graphs of vehicle parameters, actual andestimated according to an example.

FIGS. 8A-8B are various graphs of vehicle parameters, actual andestimated according to an example.

FIG. 9 shows a schematic view of a computing device for a vehicle.

DETAILED DESCRIPTION

Embodiments of the present disclosure are described herein. It is to beunderstood, however, that the disclosed embodiments are merely examplesand other embodiments can take various and alternative forms. Thefigures are not necessarily to scale; some features could be exaggeratedor minimized to show details of particular components. Therefore,specific structural and functional details disclosed herein are not tobe interpreted as limiting, but merely as a representative basis forteaching one skilled in the art to variously employ the presentinvention. As those of ordinary skill in the art will understand,various features illustrated and described with reference to any one ofthe figures can be combined with features illustrated in one or moreother figures to produce embodiments that are not explicitly illustratedor described. The combinations of features illustrated providerepresentative embodiments for typical applications. Variouscombinations and modifications of the features consistent with theteachings of this disclosure, however, could be desired for particularapplications or implementations.

The embodiments of the present disclosure generally provide for aplurality of circuits or other electrical devices. All references to thecircuits and other electrical devices and the functionality provided byeach, are not intended to be limited to encompassing only what isillustrated and described herein. While particular labels may beassigned to the various circuits or other electrical devices disclosed,such labels are not intended to limit the scope of operation for thecircuits and the other electrical devices. Such circuits and otherelectrical devices may be combined with each other and/or separated inany manner based on the particular type of electrical implementationthat is desired. It is recognized that any circuit or other electricaldevice disclosed herein may include any number of microprocessors,integrated circuits, memory devices (e.g., FLASH, random access memory(RAM), read only memory (ROM), electrically programmable read onlymemory (EPROM), electrically erasable programmable read only memory(EEPROM), or other suitable variants thereof) and software which co-actwith one another to perform operation(s) disclosed herein. In addition,any one or more of the electric devices may be configured to execute acomputer-program that is embodied in a non-transitory computer readablemedium that is programmed to perform any number of the functions asdisclosed.

As an overview, the present disclosure describes systems and methods todetermine parameters of a traction battery and to control a vehicle. Attimes direct measurement of the battery parameters cannot be performed.A battery system model is used to estimate the battery parameters. Thepresent disclosure describes various systems and methods to construct abattery system model. Such a battery system model can be used toidentify parameters of the battery in real-time. More specifically,examples of the present disclosure proposes an approach for identifyingthe battery system through subspace identification approaches combinedwith the separation of a pure dynamics part and a control throughputpart to improve the identification accuracy and to reduce the identifiedsystem order. The obtained discrete state-space model is converted tothe continuous state-space model, which can then be used to derive anexpression for battery current limit computation. Factorization, e.g.,spectral decomposition or Eigendecomposition, may then be used toprocess the continuous state-space model and to derive a generalexpression for battery current limit prediction.

An example includes using a subspace identification approach toconstruct the battery system model. The subspace identification methodmay provide some advantages, e.g., state vector x(k) and initial valuex(0) can be found from the measured data, a linear system order can bedetermined, non-linear optimization is not required, and noiseinformation is not required. An additional benefit is that subspaceidentification is less sensitive to the noise than other recursiveidentification approaches, such as the Extended Kalman Filter (EKF)techniques. Moreover, identification performance of the subspaceidentification is more robust than the EKF, since noise effects areinherently identified. In contrast, noise covariance matrices should bedetermined in the EKF to achieve the desired identification performance.

FIG. 1 depicts an example of a hybrid-electric vehicle 102, e.g.,plug-in hybrid-electric vehicle. A plug-in hybrid-electric vehicle 102may comprise one or more electric motors 104 mechanically connected to ahybrid transmission 106. In addition, the hybrid transmission 106 ismechanically connected to an engine 108. The hybrid transmission 106 mayalso be mechanically connected to a drive shaft 110 that is mechanicallyconnected to the wheels 112. The electric motors 104 can provide torqueto the wheels when the engine 108 is turned on. Electric motor 104consumes electrical energy, e.g., from a battery 114, to provide torqueto propel the vehicle 102. The electric motors 104 can providedeceleration capability when the engine 108 is turned off. The electricmotors 104 may be configured as generators and can provide fuel economybenefits by recovering energy that would normally be lost as heat in thefriction braking system. The electric motors 104 may also reducepollutant emissions since the hybrid electric vehicle 102 may beoperated in electric mode under certain conditions.

The traction battery or battery pack 114 stores energy that can be usedby the electric motors 104. A vehicle battery pack 114 typicallyprovides a high voltage DC output. The battery output is made inresponse to a battery power request, which can be calculated from thefeedforward battery power value as a function of the driver powerrequest and the engine power request, which in turn can be based on thespeed and torque determinations. The battery pack 114 is electricallyconnected to a power electronics module 116. The power electronicsmodule 116 is also electrically connected to the electric motors 104 andprovides the ability to bi-directionally transfer energy between thebattery pack 114 and the electric motors 104. For example, a typicalbattery pack 14 may provide a DC voltage while the electric motors 104may require a three-phase AC current to function. The power electronicsmodule 116 may convert the DC voltage to a three-phase AC current asrequired by the electric motors 104. In a regenerative mode, the powerelectronics module 116 will convert the three-phase AC current from theelectric motors 104 acting as generators to the DC voltage required bythe battery pack 114. The methods described herein are equallyapplicable to a pure electric vehicle or any other device using abattery pack. The battery 114 can experience degradation during certainuses of the vehicle. One use in which degradation occurs is storage at ahigh state of charge (SOC). Temperature can also be a factor indegradation Battery degradation is individualized for a specific type ofbattery. Battery degradation can include the inability of a battery 114to hold a quantity of charge, e.g., less kW-hour or amp-hours are storedin the battery 114.

In addition to providing energy for propulsion, the battery 114 (orbattery pack) may provide energy for other vehicle electrical systems. Atypical system may include a DC/DC converter module 118 that convertsthe high voltage DC output of the battery pack 114 to a low voltage DCsupply that is compatible with other vehicle loads. Other high voltageloads, such as compressors and electric heaters, may be connecteddirectly to the high-voltage bus from the battery pack 114. In a typicalvehicle, the low voltage systems are electrically connected to a 12Vbattery 120. An all-electric vehicle may have a similar architecture butwithout the engine 108.

The battery pack 114 may be recharged by an external power source 126.The battery charge storage status can be measured as state of charge.The external power source 126 may provide AC or DC power to the vehicle102 by electrically connecting through a charge port 124. The chargeport 124 may be any type of port configured to transfer power from theexternal power source 126 to the vehicle 102. The charge port 124 may beelectrically connected to a power conversion module 122. The powerconversion module may condition the power from the external power source126 to provide the proper voltage and current levels to the battery pack114. In some applications, the external power source 126 may beconfigured to provide the proper voltage and current levels to thebattery pack 114 and the power conversion module 122 may not benecessary. The functions of the power conversion module 122 may residein the external power source 126 in some applications. The vehicleengine, transmission, electric motors, battery, power conversion andpower electronics may be controlled by a powertrain control module (PCM)128.

In addition to illustrating a plug-in hybrid vehicle, FIG. 1 canillustrate a battery electric vehicle (BEV) if component 108 is removed.Likewise, FIG. 1 can illustrate a traditional hybrid electric vehicle(HEV) or a power-split hybrid electric vehicle if components 122, 124,and 126 are removed. FIG. 1 also illustrates the high voltage systemwhich includes the electric motor(s), the power electronics module 116,the DC/DC converter module 118, the power conversion module 122, and thebattery pack 114. The high voltage system and battery pack includes highvoltage components including bus bars, connectors, high voltage wires,and circuit interrupt devices.

Vehicle 100 further includes a display 130 that can show data regardingthe state of the vehicle, e.g., state of the electrical system andbattery 114, as well as vehicle use/non-use data. A data generator 135can be connected to the display to compute and organize the data for thedisplay 130. In an example, the display 130 can show the battery stateas estimated or determined as described herein.

The individual battery cells within a battery pack may be constructedfrom a variety of chemical formulations. Typical battery packchemistries may include but are not limited to lead acid, nickel cadmium(NiCd), nickel-metal hydride (NIMH), Lithium-Ion or Lithium-Ion polymer.FIG. 2 shows a typical battery pack 200 in a simple series configurationof N battery cell modules 202. The battery cell modules 202 may containa single battery cell or multiple battery cells electrically connectedin parallel. The battery pack, however, may be composed of any number ofindividual battery cells and battery cell modules connected in series orparallel or some combination thereof. A typical system may have one ormore controllers, such as a Battery Control Module (BCM) 208 thatmonitors and controls the performance of the battery pack 200. The BCM208 may monitor several battery pack level characteristics such as packcurrent measured by a current sensor 206, pack voltage 210 and packtemperature 212. The performance of the current sensor 206 may beessential, in certain arrangements, to build a reliable batterymonitoring system. The accuracy of the current sensor may be useful toestimate the battery state of charge and capacity. A current sensor mayutilize a variety of methods based on physical principles to detect thecurrent including a Hall effect IC sensor, a transformer or currentclamp, a resistor in which the voltage is directly proportional to thecurrent through it, fiber optics using an interferometer to measure thephase change in the light produced by a magnetic field, or a Rogowskicoil. In the event a battery cell is charging or discharging such thatthe current entering or exiting the battery cell exceeds a threshold,the battery control module may disconnect the battery cell via the useof a circuit interrupt device (CID) such as a fuse or circuit breaker.

In addition to the pack level characteristics, there may be battery celllevel characteristics that need to be measured and monitored. Forexample, the terminal voltage, current, and temperature of each cell maybe measured. A system may use a sensor module 204 to measure thecharacteristics of one or more battery cell modules 202. Thecharacteristics may include battery cell voltage, temperature, age,number of charge/discharge cycles, etc. Typically, a sensor module willmeasure battery cell voltage. Battery cell voltage may be voltage of asingle battery or of a group of batteries electrically connected inparallel or in series. The battery pack 200 may utilize up to N_(c)sensor modules 204 to measure the characteristics of all the batterycells 202. Each sensor module 204 may transfer the measurements to theBCM 208 for further processing and coordination. The sensor module 204may transfer signals in analog or digital form to the BCM 208. Thebattery pack 200 may also contain a battery distribution module (BDM)214 which controls the flow of current into and out of the battery pack200.

FIG. 3 shows a schematic 300 of parameter estimation. A current i 301 issupplied to the battery which results in a reference voltage v_(ref)303. The reference voltage v_(ref) 303 is the actual reference voltageat the battery. The current 301 is also supplied into the identifiedmodel of battery 310, which can be identified using the methodsdescribed herein, to output an estimated voltage {circumflex over (v)}313. The estimated voltage 313 can be used in control schemes for thevehicle as it represents the estimated value at a certain condition ofthe vehicle. The identified model 310 can be stored in memory onboardthe vehicle and be used in computations, e.g., in a module or processor,to estimate the state of the battery 114. For example, the model 310 candetermine estimated battery current limits and available power limits.

FIG. 4 shows a method flow 400 of an embodiment for battery parameterestimation. At 401, a system dynamics model of a traction battery isidentified using a battery input current profile and a battery outputvoltage profile measured within a time period. The time period can beset to a small value, e.g., 100 microseconds or a multiple of 100microseconds. The time period can also be set to a time when the batteryis not supplying current to move the vehicle or not move or power thevehicle. The time period can also be set to when the battery is notbeing charged. At 403, the identified system dynamics model istransformed to a state-space model appropriate to derive explicitexpressions for battery current limit prediction. In an example, thestate space model has a diagonal system matrix consisting essentially ofsystem Eigenvalues through the Eigendecomposition. At 405, the systemcan estimate battery current limits and available power limits using thetransformed system dynamics model. At 407, the vehicle controller(s) canoperate the traction battery according to system dynamics modelidentified using estimated battery current limits and available powerlimits.

FIG. 5 shows a method flow 500 of an embodiment for battery parameterestimation. At 501, the internal resistance of the battery R_(o) isestimated. R_(o) can be estimated from the N data obtained during theprevious time window. The previous time window can be set to a timeperiod during which the battery parameters need not be updated and canbe based on prior test data of the vehicle or based on vehicle usehistory. In an example, the estimation of R_(o) can be

$\begin{matrix}{H_{0} = {{\hat{R}}_{0} = {D = \left\{ \begin{matrix}{{\frac{1}{N}{\sum\limits_{k = 1}^{N}{\left( {v_{k} - v_{k - 1}} \right)/\left( {i_{k} - i_{k - 1}} \right)}}},} & {i_{k} \neq i_{k - 1}} \\{0,} & {i_{k} = i_{k - 1}}\end{matrix} \right.}}} & (1)\end{matrix}$

where v=v_(t)−v_(oc), with v_(t) being the battery terminal voltage andv_(oc) being the open circuit voltage. The battery system output canthen be represented by

y=v_(t)−v_(oc)−

, the state space model is expressed as

x(k+1)=A _(d) x(k)B _(d) u(k)   (2)

y(k)=C _(d) x(k)   (3)

At 503, a numerical algorithm for subspace state space systemidentification (N4SID) can then be applied. Other subspaceidentification algorithms may be used, and an N4SID is used forexemplify a subspace identification algorithm. An N4SID can estimate ann_(x) order state-space model using measured input-output data. Exampleequations for this algorithm as applied to the present battery statedetermination are

$\begin{matrix}{Z_{i} = {{Y_{i{{2i} - 1}}/\begin{pmatrix}U_{0{i - 1}} \\U_{i{{2i} - 1}} \\Y_{0{i - 1}}\end{pmatrix}} = {\begin{pmatrix}L_{i}^{1} & L_{i}^{2} & L_{i}^{3}\end{pmatrix}\begin{pmatrix}U_{0{i - 1}} \\U_{i{{2i} - 1}} \\Y_{0{i - 1}}\end{pmatrix}}}} & (4) \\{Z_{i + 1} = {Y_{{i + 1}{{2i} - 1}}/\begin{pmatrix}U_{0i} \\U_{{i + 1}{2i}} \\Y_{0i}\end{pmatrix}}} & (5) \\{{where}{{A/B} = {{{AB}^{t}\left( {BB}^{t} \right)}^{- 1}{B.}}}} & (6)\end{matrix}$

where L_(i) ¹, L_(i) ², and L_(i) ² are i-by-j matrices computed usingequation (6).

where

$\begin{matrix}{U_{0{i - 1}} = \begin{bmatrix}u_{0} & u_{1} & u_{2} & \ldots & u_{j - 1} \\u_{1} & u_{2} & u_{3} & \ldots & u_{j} \\\vdots & \vdots & \vdots & \ddots & \vdots \\u_{i - 1} & u_{i} & u_{i + 1} & \ldots & u_{i + j - 2}\end{bmatrix}} & \left( {7a} \right) \\{U_{i{{2i} - 1}} = \begin{bmatrix}u_{i} & u_{i + 1} & u_{i + 2} & \ldots & u_{i + j - 1} \\u_{i + 1} & u_{i + 2} & u_{i + 3} & \ldots & u_{i + j} \\\vdots & \vdots & \vdots & \ddots & \vdots \\u_{{2i} - 1} & u_{2i} & u_{{2i} + 1} & \ldots & u_{{2i} + j - 2}\end{bmatrix}} & \left( {7b} \right) \\{Y_{0{i - 1}} = \begin{bmatrix}y_{0} & y_{1} & y_{2} & \ldots & y_{j - 1} \\y_{1} & y_{2} & y_{3} & \ldots & y_{j} \\\vdots & \vdots & \vdots & \ddots & \vdots \\y_{i - 1} & y_{i} & y_{i + 1} & \ldots & y_{i + j - 2}\end{bmatrix}} & \left( {8a} \right) \\{Y_{i{{2i} - 1}} = \begin{bmatrix}y_{i} & y_{i + 1} & y_{i + 2} & \ldots & y_{i + j - 1} \\y_{i + 1} & y_{i + 2} & y_{i + 3} & \ldots & y_{i + j} \\\vdots & \vdots & \vdots & \ddots & \vdots \\y_{{2i} - 1} & y_{2i} & y_{{2i} + 1} & \ldots & y_{{2i} + j - 2}\end{bmatrix}} & \left( {8b} \right)\end{matrix}$

The row space of A/B is equal to the projection of the row space of Aonto the row space of B.

At 505, a singular value decomposition may be conducted, but not limitedto, by the following procedure.

Singular value decomposition is conducted as

$\begin{matrix}{{\begin{pmatrix}L_{i}^{1} & L_{i}^{3}\end{pmatrix}\begin{pmatrix}U_{0{i - 1}} \\Y_{0{i - 1}}\end{pmatrix}} = {\begin{pmatrix}U_{1} & U_{2}\end{pmatrix}\begin{pmatrix}\sum_{1} & 0 \\0 & 0\end{pmatrix}V^{t}}} & (9)\end{matrix}$

where Γ_(i)=U₁Σ₁ ^(1/2), and Γ_(i−1)=U¹⁻Σ₁ ^(1/2).

System matrices are computed from

$\begin{matrix}{\begin{pmatrix}{\Gamma_{i - 1}^{*}Z_{i + 1}} \\Y_{ii}\end{pmatrix} = {{\begin{pmatrix}K_{11} & K_{12} \\K_{21} & K_{22}\end{pmatrix} \cdot \begin{pmatrix}{\Gamma_{i}^{*}Z_{i}} \\U_{i{{2i} - 1}}\end{pmatrix}} + \begin{pmatrix}\rho_{1} \\\rho_{2}\end{pmatrix}}} & (10)\end{matrix}$

Matrices of the identified discrete state space model are determined asA_(d)=K₁₁, B_(d)=K₂₁ and C_(d), D_(d) are from K₁₂ and K₂₂,respectively.

In another example, the matrices can be determined via a different N4SIDalgorithm, e.g., an approximation solution. Firstly the states {tildeover (X)}_(i) and {tilde over (X)}_(i+1) are determines, e.g., using thefollowing equations:

$\begin{matrix}{{\overset{\sim}{X}}_{i} = {{\Gamma_{i}^{*}\begin{pmatrix}\Gamma_{i}^{1} & \Gamma_{i}^{3}\end{pmatrix}}\begin{pmatrix}U_{0{i - 1}} \\Y_{0{i - 1}}\end{pmatrix}}} & \left( {11a} \right) \\{{\overset{\sim}{X}}_{i + 1} = {{\Gamma_{i + 1}^{*}\begin{pmatrix}\Gamma_{i + 1}^{1} & \Gamma_{i + 1}^{3}\end{pmatrix}}\begin{pmatrix}U_{0i} \\Y_{0i}\end{pmatrix}}} & \left( {11b} \right)\end{matrix}$

Then the least squares solution is applied

$\begin{matrix}{\begin{pmatrix}{\overset{\sim}{X}}_{i + 1} \\Y_{ii}\end{pmatrix} = {{\begin{pmatrix}{\overset{\sim}{L}}_{11} & {\overset{\sim}{L}}_{12} \\{\overset{\sim}{L}}_{21} & {\overset{\sim}{L}}_{22}\end{pmatrix} \cdot \begin{pmatrix}{\overset{\sim}{X}}_{i} \\U_{ii}\end{pmatrix}} + \begin{pmatrix}\rho_{1} \\\rho_{2}\end{pmatrix}}} & (12)\end{matrix}$

At 507, the matrices can be approximated as follows:

$\begin{matrix}{\begin{pmatrix}A_{d} & B_{d\;} \\C_{d} & D_{d}\end{pmatrix} = \begin{pmatrix}{\overset{\sim}{L}}_{11} & {\overset{\sim}{L}}_{12} \\{\overset{\sim}{L}}_{21} & {\overset{\sim}{L}}_{22}\end{pmatrix}} & (13)\end{matrix}$

Thus, the state-space matrices A_(d) , B_(d) , C_(d), and D_(d) are nowidentified. From these the expression of the current limit from thebattery can be identified.

At 509, the discrete state-space matrices are converted to continuousmatrices.

From the continuous state-space expression

{dot over (x)}=Λx+Bu

y=Cx+Du′  (14)

the discrete model is expressed as

$\begin{matrix}\begin{matrix}{x_{k + 1} = {{\left( {I + {A\; \Delta \; t}} \right)x_{k}} + {B\; \Delta \; {tu}_{k}}}} \\{= {{A_{d}x_{k}} + {B_{d}u_{k}}}}\end{matrix} & (15) \\\begin{matrix}{y_{k} = {{Cx}_{k} + {Du}_{k}}} \\{= {{C_{d}x_{k}} + {D_{d}u_{k}}}}\end{matrix} & \;\end{matrix}$

From the identified A_(d), B_(d), C_(d), and D_(d), a continuousstate-space model is derived as

A=(A _(d) −I)/Δt, B=B _(d) /Δt , C=C _(d), and D=D.

Once converted to continuous form, Eigendecomposition is performed, at511. The equation for Eigendecomposition can be

A=QAQ ⁻¹,   (16)

where Q is the n×n matrix whose i-th column is the basis Eigen vectorq_(i). Λ is the diagonal matrix whose diagonal elements arecorresponding Eigenvalues.

The transformed state vector expressed by the Eigenvectors is computedby {tilde over (x)}=Q⁻¹ x.

At 513, the transformed state-space matrices are determined by

$\begin{matrix}{\overset{\sim}{A} = \Lambda} & \left( {17a} \right) \\{\overset{\sim}{B} = {Q^{- 1}B}} & \left( {17b} \right) \\{\overset{\sim}{C} = {CQ}} & \left( {17c} \right) \\{\overset{\sim}{D} = D} & \left( {17d} \right) \\{{where}{\Lambda = {\begin{bmatrix}\lambda_{1} & 0 & \ldots & \; & 0 \\0 & \ddots & \ddots & \; & \; \\\vdots & \ddots & \lambda_{i} & \; & \vdots \\\; & \; & \; & \ddots & 0 \\0 & \; & \ldots & 0 & \lambda_{n\;}\end{bmatrix}\quad}}} & (18)\end{matrix}$

Now that the transformed state-space matrices are set, the battery modelis identified, e.g., at 515. This can be done with the followingequations

$\begin{matrix}{{\overset{.}{\overset{\sim}{x}}}_{i} = {{{- \lambda_{i}}{\overset{\sim}{x}}_{i}} + {{\overset{\sim}{B}}_{i,1}u}}} & \left( {19a} \right) \\{y = {{\sum\limits_{i}{{\overset{\sim}{C}}_{1,x}{\overset{\sim}{x}}_{i}}} + {\overset{\sim}{D}u}}} & \left( {19b} \right)\end{matrix}$

where y=v_(oc)−v_(t) =v₁+v₂ and u=i.

As a result and at 515, the battery current limits during the timeduration t=t_(d) can be computed by

$\begin{matrix}{i = \frac{v_{oc} - v_{\lim} - {\sum\limits_{i}^{n}{{\overset{\sim}{C}}_{1,i}{\overset{\sim}{x}}_{i,0}e^{{- \lambda_{i}}t_{d}}}}}{R_{0} - {\sum\limits_{i}^{n}{{{\overset{\sim}{C}}_{1,i}\left( {1 - e^{{- \lambda_{i}}t_{d}}} \right)}\frac{{\overset{\sim}{B}}_{i,1}}{\lambda_{i}}}}}} & (20)\end{matrix}$

where v_(lim) is the battery voltage limit. v_(lim)=v_(lb) (batterylower voltage limit) for discharging, and v_(lim)=v_(ub) (battery uppervoltage limit) for charging.

When n=2, the equation is expressed as

$\begin{matrix}{i = \frac{v_{oc} - v_{\lim} - {{\overset{\sim}{C}}_{1,1}{\overset{\sim}{x}}_{1,0}e^{{- \lambda_{1}}t_{d}}} - {{\overset{\sim}{C}}_{1,2}{\overset{\sim}{x}}_{2,0}e^{{- \lambda_{2}}t_{d}}}}{R_{0} - {{{\overset{\sim}{C}}_{1,1}\left( {1 - e^{{- \lambda_{1}}t_{d}}} \right)}\frac{{\overset{\sim}{B}}_{1,1}}{\lambda_{1}}} - {{{\overset{\sim}{C}}_{2,1}\left( {1 - e^{{- \lambda_{2}}t_{d}}} \right)}\frac{{\overset{\sim}{B}}_{2,1}}{\lambda_{2}}}}} & (21)\end{matrix}$

The power limit can be calculated by the following for the charge stateand the discharge state of the battery:

P_(lim)=|i_(min)|v_(ub)

P_(lim)=|i_(max)|v_(lb,)

where P_(lim) is the power capability, v_(ub) is the battery uppervoltage limit, and i_(min) is the absolute minimum current. In thedischarge state, i_(max) is the maximum current that can be drawn fromthe battery. Thus the system may calculate the battery instantaneouspower capabilities during a charge event or discharge event.

At 517, the decision whether the battery model parameters need to beupdated is made. This can be decision can be triggered based on timesince the last update. In another example, the vehicle condition or usecan be used to trigger the update.

FIG. 6A shows a graph of battery current input into the battery as afunction of time with amps on the y-axis and time on the x-axis.

FIG. 6B show graph of battery terminal voltage at the battery as afunction of time with volts on the y-axis and time on the x-axis.

FIG. 6C shows a graph of estimated internal battery state {tilde over(x)}₁ in the battery as a function of time with volts on the y-axis andtime on the x-axis.

FIG. 6B show graph of estimated internal battery state {tilde over (x)}²in the battery as a function of time with volts on the y-axis and timeon the x-axis.

FIG. 7A shows a graph of battery input current as a function of time.

FIG. 7B shows a graph of battery voltage, as both v_(ref) and a modelvoltage v_ref=v_t−v_oc−R_(—)0*i. The label of y axis in FIG. 7B isv_t−v_oc−R_(—)0*i._(—) as a function of time. As shown the modelvoltage, shown in dashed line, closely follows the reference voltagev_(ref). For example, the Y scale is not large enough to show theidentified battery model to be different than the reference signal.

FIG. 8A shows a graph of the calculated battery maximum dischargecurrent as a function of time. This calculation is performed using thestructures and methods described herein. This graph and its underlyingdata can be used to control operation of a vehicle, e.g., an HEV 102.

FIG. 8B shows a graph of the calculated battery maximum charge currentas a function of time. This calculation is performed using thestructures and methods described herein. This graph and its underlyingdata can be used to control operation of a vehicle, e.g., an HEV 102.

FIG. 9 shows a diagrammatic representation of machine in the exampleform of a computer system 900 within which a set of instructions may beexecuted causing the machine to perform any one or more of the methods,processes, operations, or methodologies discussed herein. The HEV 102can operate on one or more computer systems 900. The HEV 102 can includethe functionality of one or more computer systems 900 or parts of thecomputer system 900.

In an example embodiment, the machine operates as a standalone device ormay be connected (e.g., networked) to other machines. In a networkeddeployment, the machine may operate in the capacity of a server or aclient machine in server-client network environment, or as a peermachine in a peer-to-peer (or distributed) network environment. Themachine may be similar to or includes components of a server computer, aclient computer, a personal computer (PC), a tablet PC, a set-top box(STB), a Personal Digital Assistant (PDA), a cellular telephone, a webappliance, a network router, switch or bridge, or any machine capable ofexecuting a set of instructions (sequential or otherwise) that specifyactions to be taken by that machine. Further, while only a singlemachine is illustrated, the term “machine” shall also be taken toinclude any collection of machines that individually or jointly executea set (or multiple sets) of instructions to perform any one or more ofthe methodologies discussed herein.

The example computer system 900 includes at least one processor 902(e.g., a central processing unit (CPU) a graphics processing unit (GPU),auxiliary processors or combinations thereof), a main memory 908 and astatic memory 914, which communicate with each other via a bus 928. Thecomputer system 900 may further include a video display 906 (e.g., aliquid crystal display (LCD), light emitting diode (LED) or a cathoderay tube (CRT)). The display 906 can be on the vehicle driver instrumentpanel or otherwise mounted in the vehicle. The computer system 900 alsoincludes an alphanumeric input device 912 (e.g., a keyboard or touchpadpresenting a keyboard), a cursor control device 916 (e.g., a mouse,touch screen, joystick, track pad or the like), a drive unit 920, asignal generation device 926 (e.g., a speaker, horn or tone generator)and a network interface device 918.

The drive unit 920 includes a machine-readable medium 922 on which isstored one or more sets of instructions 910 (e.g., software) embodyingany one or more of the methodologies or functions described herein. Theinstructions 910 may also reside, completely or at least partially,within the main memory 904 and/or within the processor 902 duringexecution thereof by the computer system 900. The main memory 908 andthe processor 902 also constituting machine-readable media.

The software, e.g., instructions 910, may further be transmitted orreceived over a network 924 via the network interface device 918 viacommunication protocols that can code and decode data for transmission.The software instructions 910 can also be communicated over the bus 928.

While the machine-readable medium, e.g., element 922, is shown in anexample embodiment to be a single medium, the term “machine-readablemedium” should be taken to include a single medium or multiple media(e.g., a centralized or distributed database, and/or associated cachesand servers) that store the one or more sets of instructions. The term“machine-readable medium” shall also be taken to include any medium thatis capable of storing, encoding or carrying a set of instructions forexecution by the machine and that cause the machine to perform any oneor more of the methodologies of the embodiments of the presentinvention. Such media can include tangible media. The term“machine-readable medium” shall accordingly be taken to include, but notbe limited to, buses, tangible carrier wave signals, solid-statememories, and optical and magnetic media

In electrified vehicle applications, power capability prediction inreal-time is important for preventing battery damage and failure modescaused by overcharging and over-discharging. A battery can be modeled toallow battery management system, e.g., the vehicle processors,circuitry, modules or controller, to reduce the likelihood of damage orfailure. A battery management system in electrified vehicleapplications, such as Electric Vehicle (EV), Plug-in Hybrid ElectricVehicle (PHEV), and Full Hybrid Electric Vehicle (FHEV) may use batterymodel identification. However, the battery model identification needsnot to be continuously executed, since the model parameter change is notso fast continuously. Thus, if the battery model identification can beexecuted on demand. However, the identification process should be donewithin a short period and in real-time once started, so that simpler andmore efficient computational schemes can be used as the process iscarried out on the vehicle. The present disclosure describes an approachfor identifying the battery system through subspace identificationapproaches.

The battery model identification as described herein uses using statespace identification (SSID). However, if the battery voltage data aredirectly used for the SSID, the order of the identified system tends tobe higher to reproduce the original battery response. As describedherein the battery system dynamics can be expressed without throughputof the current. Battery system can be modeled including an internalresistance R₀, which is typically represented as D matrix that is notused in SSID. By extracting this from the system response for SSID, itis believed that the system model can be identified with a simpler fromand improved accuracy. As a result, the identification problem isseparated into two parts: R₀ estimation and system dynamics estimation.

While exemplary embodiments are described above, it is not intended thatthese embodiments describe all possible forms of the invention. Rather,the words used in the specification are words of description rather thanlimitation, and it is understood that various changes may be madewithout departing from the spirit and scope of the invention.Additionally, the features of various implementing embodiments may becombined to form further embodiments of the invention.

What is claimed is:
 1. A vehicle comprising: a traction batteryincluding a plurality of cells; and at least one controller programmedto implement a state estimator configured to output battery state basedon internal resistance of the traction battery and a system dynamicsestimation of the traction battery that uses discrete batterymeasurements of voltage and internal resistance, and operate thetraction battery according to output of the state estimator.
 2. Thevehicle of claim 1 wherein the system dynamics estimation applies asubspace identification algorithm to approximate system matrices.
 3. Thevehicle of claim 2 wherein the controller uses the system matrices toderive expressions to estimate current limits from system matricestransformed using Eigendecomposition from the approximated systemmatrices from the subspace identification algorithm.
 4. The vehicle ofclaim 2 wherein the controller outputs a battery current limit usingestimated battery state variables and computed internal resistance. 5.The vehicle of claim 1 wherein the internal resistance is estimatedusing battery current input during a time period and a computed voltagethat is estimated from battery terminal voltage during the time period.6. The vehicle of claim 1 wherein the controller is further programmedto: estimate the internal resistance during a time period; computeprojections using a subspace identification algorithm; decomposesingular values of the computed projections; identify a discrete statespace model from the singular values; convert the discrete state spacemodel to a continuous state space model; perform Eigendecomposition of asystem matrix of the continuous state space model to a Eigendecomposedmatrix; transform a battery model with the Eigendecomposed matrix toproduce transformed matrices; and compute battery current limits basedon the transformed matrices.
 7. A vehicle comprising: a traction batteryincluding a plurality of cells; and at least one controller programmedto operate the traction battery according to battery current andavailable power limits from a state-space model derived byEigendecomposing a system dynamics model of the traction battery havinga diagonal system matrix of system Eigenvalues and identified via abattery input current profile and a battery output voltage profilemeasured within a predefined time period.
 8. The vehicle of claim 7wherein the system dynamics model comprises a system dynamics matrix, aninput matrix and an output matrix.
 9. The vehicle of claim 8 wherein thesystem dynamics model is updated in real time.
 10. The vehicle of claim7 wherein the system dynamics model is identified using a subspaceidentification algorithm.
 11. The vehicle of claim 10 wherein thesubspace identification algorithm uses a voltage profile manipulated bysubtracting a voltage drop across a battery internal resistance from thebattery output voltage profile.
 12. The vehicle of claim 11 wherein acomputed internal resistance is estimated using the battery inputcurrent profile during a time period and measured battery output voltageprofile during the time period.
 13. A method for vehicle controlcomprising: identifying a system dynamics model of a traction batteryusing a battery input current profile and a battery output voltageprofile measured within a time period; transforming the identifiedsystem dynamics model to a state-space model having a diagonal systemmatrix of system Eigenvalues through Eigendecomposition; estimating abattery current limit and an available power limit from the state spacemodel; and operating the traction battery according to the estimatedbattery current limit and available power limit.
 14. The method of claim13 wherein identifying the system dynamics model comprises identifying asystem dynamics matrix, an input matrix and an output matrix.
 15. Themethod of claim 13 wherein identifying the system dynamics modelincludes using a subspace identification algorithm.
 16. The method ofclaim 15 wherein identifying the system dynamics model includes using avoltage profile manipulated by subtracting a voltage drop across abattery internal resistance from the battery output voltage profile. 17.The method of claim 16 wherein identifying the system dynamics modelincludes estimating the internal resistance using the battery currentinput profile during a time period and measured terminal voltage profileduring the time period.
 18. The method of claim 13 wherein identifyingthe system dynamics model includes identifying the system dynamics modelin real time.